Anyone done any work on the math underlying A&A?

Odds simulators based on random number generators are OK but less than elegant solutions, and you certainly couldn’t craft a serious computer opponent from one. Rule of thumb stuff like multiply INF times 1/6 plus same for other units is OK too, but what it fails to reveal are the true overall combat results.

You know what I mean. Never mind the cost, what would you rather go into battle with? 2 subs and a battleship, or 2 battleships? The fractions add to 8/6 either way.

Solid math is what I’m looking for here. I’ve completed most of the math for a precise initial odds calculation, but I’m stuck on a final equation for the coefficients in the battle odds numerator. Anyone already been down this road?

I’m frustrated at being stuck this early, because I’m after bigger game ultimately.

The real overall battle odds are affected by this fact: in a battle that goes multiple rounds, the initial odds are changed by the outcome of the first dice roll - you go into dice roll 2 with different odds. Basically, with each round the strong get stronger and the weak get weaker.

The firepower curve is non-linear to boot. The strong get stronger faster than one might expect. That means there’s more or less a breakover point beyond which you’ve committed more resources than absolutely necessary to assure taking an objective. So what’s the least costly force needed to assure victory?

Kind of an important question when you’re spread thin and trying to take multiple objectives.

A different question along the same lines is “What will I need to take this objective at the lowest total cost?”. We’ve all noticed that more units equals fewer casulaties. The minimum force needed to take a goal is not necessarily the one that suffers the fewest casualties.

Could be an important distinction; after all, you may have to hold the ground afterward. And what will that cost? Ever seen Japan take out the Hawaiian navy, only to lose its expeditionary force to the US response? Who really won?

The mix you throw into a battle is a factor too. Some mixes have a surprisingly higher return on investment than others with exactly the same initial attack vs. defense points.

Chess pieces have rough numerical values of relative worth, but no grandmaster-level computer has ever been based on those alone. The same is true of A&A.

Anyway, there’s more, but this should be enough to kick off the topic.